Application Exponential Distribution

sessions_data <- read.csv("sessions_data.csv" )

getmode <- function(v) {
  
  x<-v
  lim.inf=min(x)-1; lim.sup=max(x)+1
  
  # hist(x,freq=FALSE,breaks=seq(lim.inf,lim.sup,0.2))
  s<-density(x,from=lim.inf,to=lim.sup,bw=0.2)
  n<-length(s$y)
  v1<-s$y[1:(n-2)];
  v2<-s$y[2:(n-1)];
  v3<-s$y[3:n]
  ix<-1+which((v1<v2)&(v2>v3))
  
  #lines(s$x,s$y,col="red")
  #points(s$x[ix],s$y[ix],col="blue")
  
  md <- s$x[which(s$y==max(s$y))] 
  
  md
}

#Data Visualization

userSessions <- sessions_data
 p <-userSessions %>% filter(username ==103)%>%select(duration)  %>% ggplot(aes(duration)) + 
   geom_histogram() 
   ggplotly(p)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

NA

for each user sessions-duration 1. Calculate p-value 2. estimate rate parameter

# library(EnvStats)
# library(exptest)
# 
# 
# usersIds <- userSessions %>% group_by(username) %>%
#   summarize(n = n()) %>% 
#   filter(n>100) %>% select(username) %>% slice_head(n=4500)
# 
#    results = NULL
#   
# for(id in usersIds$username) {
# 
#     print(id)
#     print(Sys.time())
#      print("-------------")
#   signleUserData <- userSessions %>% filter(username==id)%>%select(duration)
#   
#  
# 
#  data_with_contamination <-  signleUserData$duration
#      
#     #Code To Handling outlier 
#     q1 <- quantile(data_with_contamination  , c(.25))[["25%"]]
#     q3 <- quantile(data_with_contamination  , c(.75))[["75%"]]
#     IQR <- q3-q1
#     lower  = q1 - 1.5*IQR
#     upper = q3 + 1.5*IQR
#     
#     
#     outliers <- boxplot(data_with_contamination, plot=FALSE)$out
#     outliersPos <- which(data_with_contamination %in% outliers)
#     data_AfterDelete_Outliers <-  data_with_contamination[-outliersPos]
#     
#     outliersPro = length(outliers)/length(data_with_contamination)
#     
#     
#     dataAfterHandling_Q_b_F_C <- data_with_contamination
#     dataAfterHandling_mean <- data_with_contamination
#     dataAfterHandling_median <- data_with_contamination
#     dataAfterHandling_mode <- data_with_contamination
#     
#     
#     dataAfterHandling_Q_b_F_C[dataAfterHandling_Q_b_F_C<lower] <-  (lower)
#     dataAfterHandling_Q_b_F_C[dataAfterHandling_Q_b_F_C>upper] <-  (upper)
#     estimated_rate_After_Q_b_F_C <- eexp(dataAfterHandling_Q_b_F_C, ci=TRUE, conf = 0.95)$parameters[["rate"]]
#     
#     
#     mean = mean(data_AfterDelete_Outliers)
#     dataAfterHandling_mean[outliersPos] <-  (mean)
#     estimated_rate_After_mean <-  eexp(dataAfterHandling_mean, ci=TRUE, conf = 0.95)$parameters[["rate"]]
#     
#     
#     median = median(data_AfterDelete_Outliers)
#     dataAfterHandling_median[outliersPos] <-  (median)
#     estimated_rate_After_median <-  eexp(dataAfterHandling_median, ci=TRUE, conf = 0.95)$parameters[["rate"]]
#     
#     
#     # mode = getmode(data_AfterDelete_Outliers)
#     # dataAfterHandling_mode[outliersPos] <-  (mode) 
#     # estimated_rate_After_mode <- eexp(dataAfterHandling_mode, ci=TRUE, conf = 0.95)$parameters[["rate"]]
#     
#    estimated_rate_Before_Handling <- eexp(data_with_contamination, ci=TRUE, conf = 0.95)$parameters[["rate"]]
#     # 
#     
#     Q_b_F_C_P_value <-shapiro.exp.test(dataAfterHandling_Q_b_F_C  )$p.value
#     mean_P_value <-shapiro.exp.test(dataAfterHandling_mean )$p.value
#     median_P_value <-shapiro.exp.test(dataAfterHandling_median )$p.value
#     # mode_P_value <-shapiro.exp.test(dataAfterHandling_mode)$p.value
#     Before_P_value <- shapiro.exp.test(data_with_contamination  )$p.value
#       
#        results = rbind(
#       results,
#       data.frame(
#         id,
#         outliersPro,
#         estimated_rate_Before_Handling,
#         estimated_rate_After_Q_b_F_C,
#         estimated_rate_After_mean,
#         estimated_rate_After_median,
#        # estimated_rate_After_mode ,
#         Before_P_value,
#         Q_b_F_C_P_value,
#         mean_P_value,
#         median_P_value#,
#         #mode_P_value
#       ))
#   }
#   
# ```
# 
# 
# 
# ```{r}
# above_05 <- function(pValueList){
#   percent <- mean(pValueList>.05)
#   return (percent)
# }

results <- read.csv("results.csv")

#Visualization Results

results %>%   select(estimated_rate_Before_Handling , 
                     estimated_rate_After_Q_b_F_C , 
                     estimated_rate_After_mean , 
                     estimated_rate_After_median 
                     ) %>% 
  gather("Method" , "estimatedRate" , estimated_rate_Before_Handling , estimated_rate_After_Q_b_F_C , estimated_rate_After_mean ,estimated_rate_After_median  ) %>% 
  ggplot(aes(x = (estimatedRate))) + 
     geom_histogram( aes(colour = as.factor(Method))) + 

  facet_wrap(.~Method)

results %>%   select(Before_P_value , 
                     mean_P_value , 
                     median_P_value , 
                     Q_b_F_C_P_value 
                     ) %>% 
  gather("Method" , "pValue" , Before_P_value , mean_P_value , median_P_value ,Q_b_F_C_P_value  ) %>% 
  ggplot(aes(x = (pValue))) + 
     geom_histogram( ) + 
 scale_x_continuous(breaks = c(0.05)) +

  facet_wrap(.~Method)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.